The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

The differential equations that arise in practice are of two types. Here is an example of the first type. Here is an example of the second type. This equation has a symbolic ...

Here is a system of two ODEs whose coefficient matrix has real and distinct eigenvalues. This solves the system. Note that the general solution depends on two arbitrary ...

Following are two examples of nonlinear systems of ODEs that can be solved symbolically using DSolve. The first three equations in this system of four nonlinear ODEs can be ...

DSolve returns a general solution for a problem if no initial or boundary conditions are specified. The general solution to this equation is returned. However, if initial or ...

When you see a two-dimensional expression on the screen, you can edit it much as you would edit text. You can for example place your cursor somewhere and start typing. Or you ...

Primitives which can take multiple elements. Some primitives have multi-element forms that can be processed and rendered more quickly by the Mathematica front end than the ...

Eigenvalues and eigenvectors. The eigenvalues of a matrix m are the values λ_i for which one can find nonzero vectors v_i such that m.v_i λ_iv_i. The eigenvectors are the ...

Elementary transcendental functions. Mathematica gives exact results for logarithms whenever it can. Here is log_21024. You can find the numerical values of mathematical ...

Special forms for some common symbols. This is equivalent to Sin[60Degree]. Here is the long form of the input.